Modeling V1 complex cells in alert monkeys

Abstract. Cortical complex cells are usually described as nonlinear energy operators that sum squared outputs of quadrature pairs of linear subunits, responding to drifting sinusoidal gratings with unmodulated elevation of firing rate (F0 harmonic). However, several lines of evidence suggest that the view of complex cells as a uniform class is over-simplified, since energy models do not capture many complex cell behaviors. In alert monkeys complex cells with strongly overlapping increment and decrement regions exhibit a considerable F1 modulation, and a subset of these cells have a relative modulation (RM=F1/F0) >1. We have also found that most complex cells show profound dependence of the response form (harmonic content), and not only the amplitude, on grating parameters such as spatial and temporal frequency and size, displaying a variety of behaviors ranging from nonlinear unmodulated firing (F0) and frequency doubling (F2) to pseudolinear modulation (F1). One of the parsimonious explanations could be that at least some of these behaviors, e.g. F1 modulation, result from the imbalance of increment and decrement mechanisms such as incomplete spatial overlap and/or difference in amplitudes of the two regions. We tested this hypothesis using a model that approximates an apparent structure of complex receptive fields in our data by pooling two linear (increment and decrement) inputs with Gaussian spatial profile and same biphasic temporal response function. Model cells with various overlaps and amplitude ratios were stimulated with drifting gratings of different spatial frequencies. To quantify the measure of spatial (im)balance we computed a product of overlap index and amplitude ratio. In the model, maximal modulation increased with spatial imbalance, and the correlation for the two measures was high (r=-0.86, p<0.01). However, the model consistently yielded lower RM values than those in the data. Moreover, weak insignificant correlation between RM and spatial imbalance in the data for complex cells (r=-0.15, p>0.01) was inconsistent with model predictions. Thus, a static spatial imbalance of increment and decrement mechanisms cannot fully predict the presence of strong F1 harmonic in responses of complex cells. These results and effects of temporal frequency suggest that temporal properties of input channels and possibly the dynamics of interaction between them play an important role in shaping the responses of complex cells. To account for the response diversity exhibited by complex cells, we are developing more realistic models that also include influences of the surround.